Question

How do you solve $\dfrac{t}{9} - 7 = - 5$?

Answer 1

Hint: This problem deals with solving the linear equation with one variable. A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form of $ax + b = 0$, and are usually solved for the variable $x$ using basic algebraic operations.

Complete step-by-step solution:
Given a linear equation one variable, here the variable is $t$, which is considered as given below:
\[ \Rightarrow \dfrac{t}{9} - 7 = - 5\]
Now rearrange the terms such that all the constants are on one side of an equation and all the $t$terms are on the other side of the equation.
Now moving the constant -7 which is on the left hand side of the equation to the right hand side of the equation, as shown below:
\[ \Rightarrow \dfrac{t}{9} = 7 - 5\]
Now simplifying the above equation, as the like terms are and the constants are grouped together, the constants 7 and -5 are simplified on the right hand side of the equation, as shown below:
\[ \Rightarrow \dfrac{t}{9} = 2\]
Now multiplying the above equation with 9, so as the coefficient of the $t$ term on the left hand side of the equation, as shown below:
\[ \Rightarrow 9 \times \dfrac{t}{9} = 9 \times 2\]
Now simplifying the above equation, as shown:
$\therefore t = 18$

The solution of the equation $\dfrac{t}{9} - 7 = - 5$ is 18.

Note: Please note that the linear equations in one variable which are expressed in the form of $ax + b = 0$, have only one solution. Where a and b are two integers, and x is a variable. This means that there will be no terms involving higher powers of x, not even the power of 2, which is ${x^2}$.